SQL Server Management Requirments
Microsoft outlined the requirements for SQL Server Management Studio (SSMS) on the same page you mentioned (or here as well) as:
Supported Operating systems
This release of SSMS supports the following platforms when used with the latest available service pack:
Windows 10, Windows 8, Windows 8.1, Windows 7 (SP1), Windows Server 2012 (64-bit), Windows Server 2012 R2 (64-bit), Windows Server 2008 R2 (64-bit)
So Windows 7 SP1 should be fine to run the SQL Server Management Studio 2016 (the MS SQL Server Management Studio (16.5.3) can be downloaded here by the way).